About 200 patients were inside the building and an adjoining nursing home at the time. It is South Korea's deadliest fire in almost a decade and the death toll is expected to rise with several of the injured in critical condition.
Firefighters said the victims appeared to have died from smoke inhalation. Three hospital medical staff - a doctor, nurse and nursing assistant - are among the victims.
Authorities have given varying death tolls, with police earlier saying 41 had died, but fire officials and hospital sources now say at least 37 are dead.